A numerical model coupling electromagnetic field and plasma arc impact with multiphase transport phenomena such as flow, heat transfer and solidification for the vacuum arc remelting (VAR) process is proposed. 3D simulations of the VAR process for refining a Titanium-based (Ti–6Al–4V) alloy are made. Different arc distributions (diffusive, constricted centric, constricted eccentric, and rotating arcs) under an axial magnetic field (AMF) are studied, focusing on their impact on the flow patterns and the resulting melt pool of the as-solidifying ingot. Simulation results show that diffusive arc leads to a shallow symmetrical melt pool; constricted centric and rotating arcs lead to electro-vortex flow and the symmetrical melt pool; constricted eccentric leads to electro-vortex flow as well, but the deepest non-symmetrical melt pool.